(x^2-2)(x^2-2-3)=

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Solution for (x^2-2)(x^2-2-3)= equation:


Simplifying
(x2 + -2)(x2 + -2 + -3) = 0

Reorder the terms:
(-2 + x2)(x2 + -2 + -3) = 0

Reorder the terms:
(-2 + x2)(-2 + -3 + x2) = 0

Combine like terms: -2 + -3 = -5
(-2 + x2)(-5 + x2) = 0

Multiply (-2 + x2) * (-5 + x2)
(-2(-5 + x2) + x2(-5 + x2)) = 0
((-5 * -2 + x2 * -2) + x2(-5 + x2)) = 0
((10 + -2x2) + x2(-5 + x2)) = 0
(10 + -2x2 + (-5 * x2 + x2 * x2)) = 0
(10 + -2x2 + (-5x2 + x4)) = 0

Combine like terms: -2x2 + -5x2 = -7x2
(10 + -7x2 + x4) = 0

Solving
10 + -7x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x2)(5 + -1x2) = 0


Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}

Subproblem 2
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {-1.414213562, 1.414213562, -2.236067978, 2.236067978}

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